Copyright	(c) Fabricio Olivetti 2021 - 2021
License	BSD3
Maintainer	fabricio.olivetti@gmail.com
Stability	experimental
Portability	FlexibleInstances, DeriveFunctor, ScopedTypeVariables, ConstraintKinds
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.SRTree

Description

Expression tree for Symbolic Regression

Synopsis

data SRTree val
- = Var Int
- | Param Int
- | Const Double
- | Uni Function val
- | Bin Op val val
data Function
- = Id
- | Abs
- | Sin
- | Cos
- | Tan
- | Sinh
- | Cosh
- | Tanh
- | ASin
- | ACos
- | ATan
- | ASinh
- | ACosh
- | ATanh
- | Sqrt
- | Cbrt
- | Square
- | Log
- | Exp
data Op
- = Add
- | Sub
- | Mul
- | Div
- | Power
param :: Int -> Fix SRTree
var :: Int -> Fix SRTree
arity :: Fix SRTree -> Int
getChildren :: Fix SRTree -> [Fix SRTree]
countNodes :: Fix SRTree -> Int
countVarNodes :: Fix SRTree -> Int
countConsts :: Fix SRTree -> Int
countParams :: Fix SRTree -> Int
countOccurrences :: Int -> Fix SRTree -> Int
deriveBy :: Bool -> Int -> Fix SRTree -> Fix SRTree
deriveByVar :: Int -> Fix SRTree -> Fix SRTree
deriveByParam :: Int -> Fix SRTree -> Fix SRTree
derivative :: Floating a => Function -> a -> a
forwardMode :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> [a]
gradParams :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> (a, [a])
evalFun :: Floating a => Function -> a -> a
evalOp :: Floating a => Op -> a -> a -> a
inverseFunc :: Function -> Function
evalTree :: (Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> a
relabelParams :: Fix SRTree -> Fix SRTree
constsToParam :: Fix SRTree -> (Fix SRTree, [Double])
floatConstsToParam :: Fix SRTree -> (Fix SRTree, [Double])

Documentation

data SRTree val Source #

Tree structure to be used with Symbolic Regression algorithms. This structure is a fixed point of a n-ary tree.

Constructors

Var Int	index of the variables
Param Int	index of the parameter
Const Double	constant value, can be converted to a parameter
Uni Function val	univariate function
Bin Op val val	binary operator

Instances

Instances details

Functor SRTree Source #
Instance details Defined in Data.SRTree.Internal Methods fmap :: (a -> b) -> SRTree a -> SRTree b # (<$) :: a -> SRTree b -> SRTree a #
Floating (Fix SRTree) Source #
Instance details Defined in Data.SRTree.Internal Methods pi :: Fix SRTree # exp :: Fix SRTree -> Fix SRTree # log :: Fix SRTree -> Fix SRTree # sqrt :: Fix SRTree -> Fix SRTree # (**) :: Fix SRTree -> Fix SRTree -> Fix SRTree # logBase :: Fix SRTree -> Fix SRTree -> Fix SRTree # sin :: Fix SRTree -> Fix SRTree # cos :: Fix SRTree -> Fix SRTree # tan :: Fix SRTree -> Fix SRTree # asin :: Fix SRTree -> Fix SRTree # acos :: Fix SRTree -> Fix SRTree # atan :: Fix SRTree -> Fix SRTree # sinh :: Fix SRTree -> Fix SRTree # cosh :: Fix SRTree -> Fix SRTree # tanh :: Fix SRTree -> Fix SRTree # asinh :: Fix SRTree -> Fix SRTree # acosh :: Fix SRTree -> Fix SRTree # atanh :: Fix SRTree -> Fix SRTree # log1p :: Fix SRTree -> Fix SRTree # expm1 :: Fix SRTree -> Fix SRTree # log1pexp :: Fix SRTree -> Fix SRTree # log1mexp :: Fix SRTree -> Fix SRTree #
Num (Fix SRTree) Source #
Instance details Defined in Data.SRTree.Internal Methods (+) :: Fix SRTree -> Fix SRTree -> Fix SRTree # (-) :: Fix SRTree -> Fix SRTree -> Fix SRTree # (*) :: Fix SRTree -> Fix SRTree -> Fix SRTree # negate :: Fix SRTree -> Fix SRTree # abs :: Fix SRTree -> Fix SRTree # signum :: Fix SRTree -> Fix SRTree # fromInteger :: Integer -> Fix SRTree #
Fractional (Fix SRTree) Source #
Instance details Defined in Data.SRTree.Internal Methods (/) :: Fix SRTree -> Fix SRTree -> Fix SRTree # recip :: Fix SRTree -> Fix SRTree # fromRational :: Rational -> Fix SRTree #
Show val => Show (SRTree val) Source #
Instance details Defined in Data.SRTree.Internal Methods showsPrec :: Int -> SRTree val -> ShowS # show :: SRTree val -> String # showList :: [SRTree val] -> ShowS #
Eq val => Eq (SRTree val) Source #
Instance details Defined in Data.SRTree.Internal Methods (==) :: SRTree val -> SRTree val -> Bool # (/=) :: SRTree val -> SRTree val -> Bool #
Ord val => Ord (SRTree val) Source #
Instance details Defined in Data.SRTree.Internal Methods compare :: SRTree val -> SRTree val -> Ordering # (<) :: SRTree val -> SRTree val -> Bool # (<=) :: SRTree val -> SRTree val -> Bool # (>) :: SRTree val -> SRTree val -> Bool # (>=) :: SRTree val -> SRTree val -> Bool # max :: SRTree val -> SRTree val -> SRTree val # min :: SRTree val -> SRTree val -> SRTree val #

data Function Source #

Supported functions

Constructors

Id
Abs
Sin
Cos
Tan
Sinh
Cosh
Tanh
ASin
ACos
ATan
ASinh
ACosh
ATanh
Sqrt
Cbrt
Square
Log
Exp

Instances

Instances details

Enum Function Source #
Instance details Defined in Data.SRTree.Internal Methods succ :: Function -> Function # pred :: Function -> Function # toEnum :: Int -> Function # fromEnum :: Function -> Int # enumFrom :: Function -> [Function] # enumFromThen :: Function -> Function -> [Function] # enumFromTo :: Function -> Function -> [Function] # enumFromThenTo :: Function -> Function -> Function -> [Function] #
Read Function Source #
Instance details Defined in Data.SRTree.Internal Methods readsPrec :: Int -> ReadS Function # readList :: ReadS [Function] # readPrec :: ReadPrec Function # readListPrec :: ReadPrec [Function] #
Show Function Source #
Instance details Defined in Data.SRTree.Internal Methods showsPrec :: Int -> Function -> ShowS # show :: Function -> String # showList :: [Function] -> ShowS #
Eq Function Source #
Instance details Defined in Data.SRTree.Internal Methods (==) :: Function -> Function -> Bool # (/=) :: Function -> Function -> Bool #
Ord Function Source #
Instance details Defined in Data.SRTree.Internal Methods compare :: Function -> Function -> Ordering # (<) :: Function -> Function -> Bool # (<=) :: Function -> Function -> Bool # (>) :: Function -> Function -> Bool # (>=) :: Function -> Function -> Bool # max :: Function -> Function -> Function # min :: Function -> Function -> Function #

data Op Source #

Supported operators

Constructors

Add
Sub
Mul
Div
Power

Instances

Instances details

Enum Op Source #
Instance details Defined in Data.SRTree.Internal Methods succ :: Op -> Op # pred :: Op -> Op # toEnum :: Int -> Op # fromEnum :: Op -> Int # enumFrom :: Op -> [Op] # enumFromThen :: Op -> Op -> [Op] # enumFromTo :: Op -> Op -> [Op] # enumFromThenTo :: Op -> Op -> Op -> [Op] #
Read Op Source #
Instance details Defined in Data.SRTree.Internal Methods readsPrec :: Int -> ReadS Op # readList :: ReadS [Op] # readPrec :: ReadPrec Op # readListPrec :: ReadPrec [Op] #
Show Op Source #
Instance details Defined in Data.SRTree.Internal Methods showsPrec :: Int -> Op -> ShowS # show :: Op -> String # showList :: [Op] -> ShowS #
Eq Op Source #
Instance details Defined in Data.SRTree.Internal Methods (==) :: Op -> Op -> Bool # (/=) :: Op -> Op -> Bool #
Ord Op Source #
Instance details Defined in Data.SRTree.Internal Methods compare :: Op -> Op -> Ordering # (<) :: Op -> Op -> Bool # (<=) :: Op -> Op -> Bool # (>) :: Op -> Op -> Bool # (>=) :: Op -> Op -> Bool # max :: Op -> Op -> Op # min :: Op -> Op -> Op #

param :: Int -> Fix SRTree Source #

create a tree with a single node representing a parameter

var :: Int -> Fix SRTree Source #

create a tree with a single node representing a variable

arity :: Fix SRTree -> Int Source #

Arity of the current node

getChildren :: Fix SRTree -> [Fix SRTree] Source #

Get the children of a node. Returns an empty list in case of a leaf node.

countNodes :: Fix SRTree -> Int Source #

Count the number of nodes in a tree.

countVarNodes :: Fix SRTree -> Int Source #

Count the number of Var nodes

countConsts :: Fix SRTree -> Int Source #

Count the number of const nodes

countParams :: Fix SRTree -> Int Source #

Count the number of Param nodes

countOccurrences :: Int -> Fix SRTree -> Int Source #

Count the occurrences of variable indexed as ix

deriveBy :: Bool -> Int -> Fix SRTree -> Fix SRTree Source #

Creates the symbolic partial derivative of a tree by variable dx (if p is False) or parameter dx (if p is True).

deriveByVar :: Int -> Fix SRTree -> Fix SRTree Source #

Symbolic derivative by a variable

deriveByParam :: Int -> Fix SRTree -> Fix SRTree Source #

Symbolic derivative by a parameter

derivative :: Floating a => Function -> a -> a Source #

forwardMode :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> [a] Source #

Calculates the numerical derivative of a tree using forward mode provided a vector of variable values xss, a vector of parameter values theta and a function that changes a Double value to the type of the variable values.

gradParams :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> (a, [a]) Source #

The function gradParams calculates the numerical gradient of the tree and evaluates the tree at the same time. It assumes that each parameter has a unique occurrence in the expression. This should be significantly faster than forwardMode.

evalFun :: Floating a => Function -> a -> a Source #

evalOp :: Floating a => Op -> a -> a -> a Source #

inverseFunc :: Function -> Function Source #

Returns the inverse of a function. This is a partial function.

evalTree :: (Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> a Source #

Evaluates the tree given a vector of variable values, a vector of parameter values and a function that takes a Double and change to whatever type the variables have. This is useful when working with datasets of many values per variables.

relabelParams :: Fix SRTree -> Fix SRTree Source #

Relabel the parameters incrementaly starting from 0

constsToParam :: Fix SRTree -> (Fix SRTree, [Double]) Source #

Change constant values to a parameter, returning the changed tree and a list of parameter values

floatConstsToParam :: Fix SRTree -> (Fix SRTree, [Double]) Source #

Same as constsToParam but does not change constant values that can be converted to integer without loss of precision